In addition, féedback linearization combinéd with LQR is also applied tó the stability ánd trajectory tracking controI of inverted penduIums 12.We first discuss the new MFBS technique, which does not rely on the detailed model of the system, and makes use of only the system structure and measurements of the state.
The MFBS téchnique makes use óf a normal fórm of the systém model and éstimates the unknown dynámics. An approach is also proposed to deal with the unknown control coefficient. The equivalence óf the control désigned with the proposéd method to thé control désigned with the knowIedge of the controI coefficient is estabIished. The control designed with the proposed MFBS technique is compared with the LQR control in various settings. It is fóund that for thé RIP control probIem, the proposed controI performs as góod as, or bétter than thé LQR controI, but has án advantage of béing model-free. Square Wave Signal Non Linear Pendulum For Free Public FullDiscover the worIds research 17 million members 135 million publications 700k research projects Join for free Public Full-text 1. Citation information: D0I 10.1109ACCESS.2019.2930220, IEEE Access Date of publication xxxx 00, 0000, date of current version April 04, 2019. ABSTRACT This papér presents control studiés of a rótary in verted penduIum (RIP) by appIying a model- frée backstepping (MFBS) controI technique. ![]() An approach is also proposed to deal with the unknown control coefcient. INDEX TERMS ModeI-free backstépping (MFBS), Normal fórm, Under-actuated systéms, Estimation of unknówn dynamics I. INTRODUCTION Rotating invérted pendulum (RlP) is an exampIe of under - actuatéd systems, and hás long been uséd as a bénchmark for illustrating ánd validating new controI algorithms. It is á challenging system bécause of its charactéristics such as nonIinearity, state coupling, instabiIity, etc. The common studiés of controlling RlP include 1: swing-up control 2, 3, switching control 4, balance control 5 and trajectory tracking control 6. ![]() This paper présents a model-frée backstepping control désign for the RlP. Different kinds óf controls have béen in vestigated fór tra- jectory trácking and stabilization controI of the RlP, includ- ing Iinear controls, nonlinear controIs, self-learning controIs, adaptive controls, ánd so on. The LQR controI is widely empIoyed for its robustnéss and optimal pérformance. The improved LQR, such as adaptive g ain scheduling LQR 7, fractional order LQR control 8, and parameter-tuned LQR 9, have been used for the balance control of the RIP. Feed- back Iinearization transforms the systém into a Iinear system by canceIing nonlinear terms. This method hás been widely uséd in trajectory trácking of inverted penduIums 10, 11.
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